Question: 7 people can paint 5 walls in 30 minutes. How many minutes will it take for 10 people to paint 7 walls? Round to the nearest minute.
Solution: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 5\text{ walls}\\ p &= 7\text{ people}\\ t &= 30\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{5}{30 \cdot 7} = \dfrac{1}{42}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 7 walls with 10 people. $t = \dfrac{w}{r \cdot p} = \dfrac{7}{\dfrac{1}{42} \cdot 10} = \dfrac{7}{\dfrac{5}{21}} = \dfrac{147}{5}\text{ minutes}$ $= 29 \dfrac{2}{5}\text{ minutes}$ Round to the nearest minute: $t = 29\text{ minutes}$